Lots of threads in PPRuNe talk to this topic.
Suggest you run a search on something like "takeoff weight limit" and have a read through the resulting links. Be aware that references to "mass" and "weight" are sensibly similar and relate to the practices adopted by particular States.
However, in addition to FE Hoppy's observations, the 10 second short brief is ..
(a) the certificated (ie TC and AFM) MTOW is the maximum weight for which all the relevant Design Standard requirements can be met. Often the limiting case either will be one of the structural considerations or one of the WAT limits.
The certificated MTOW is just that - regardless of the circumstances, the pilot may not takeoff at a weight in excess of the MTOW. Caveat - the Regulator may authorise occasional higher takeoff weights for special purposes, eg a ferry flight overseas to permit the carriage of additional temporary tankage fuel.
(b) on a day to day basis the MTOW may have to be reduced (and usually is) by one of a range of considerations. Often such a reduced weight limit will be referred to by other terms, eg RTOW (regulated TOW).
These other limits may be performance requirements (eg WAT limits, OEI obstacle climb, AEO/OEI runway distance limits, etc.), system limitations (eg brake energy limit), cruise limits (eg weight limitation to achieve a high LSA AEO/OEI), destination limits (eg runway or climb limit weight plus expected fuel burn).
The number of engines only changes the numbers, otherwise the philosophy is similar.